Question

Calculate the sum of the infinite series: $1-\frac{1}{3}+\frac{1}{9}-\frac{1}{27}+.....$.

• A. $\frac{2}{3}$
• B. $\frac{3}{4}$
• C. $1$
• D. $\frac{4}{3}$
• E. $\frac{3}{2}$

Answer 1

Answer: (B)

$\frac{3}{4}$

Given series is $1,-\frac{1}{3},+\frac{1}{9},-\frac{1}{27}......................$

Then common ratio $=$ $(-\frac{1}{3})/1=-\frac{1}{3}$

Then sum of infinite series $S=$ $\frac{a_1}{1-r}=\frac{1}{1-(-\frac{1}{3})}=\frac{1}{\frac{1+3}{3}}=\frac{3}{4}$